Magnonic holographic memory and methods

ABSTRACT

An electronic device using an array of magnetic wave guides is shown. In one example a memory device is shown that utilizes spin waves and a magnet storage element that interacts with the spin waves. In one example, an electronic device is shown that utilizes both a complementary metal oxide device and a magnonic device coupled together.

CLAIM OF PRIORITY

This application claims the benefit priority to U.S. Provisional PatentApplication No. 62/069,617, filed Oct. 28, 2014, which is incorporatedherein by reference in its entirety.

TECHNICAL FIELD

This invention relates to computer memory and associated methods.

Specific examples include magnonic holographic memory devices.

BACKGROUND

Existing computer memory devices, such as CMOS memory devices can bechallenged in selected operations, such as image processing, speechrecognition, etc. Improved memory devices are desired with improvedcharacteristics such as increased speed and reduced power consumption.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a mangnonic device according to an example of theinvention.

FIG. 2 shows a schematic of a mangnonic device according to an exampleof the invention.

FIG. 3 shows a four arm example of a mangnonic device according to anexample of the invention.

FIG. 4 shows another four arm example mangnonic device according to anexample of the invention.

FIG. 5 shows a double cross example of a mangnonic device according toan example of the invention.

FIG. 6 shows experimental operating data of a mangnonic device accordingto an example of the invention.

FIG. 7 shows additional experimental operating data of a mangnonicdevice according to an example of the invention.

FIG. 8 shows another double cross example of a mangnonic deviceaccording to an example of the invention.

FIG. 9 shows one method according to an example of the invention.

FIG. 10 shows an electronic device incorporating a magnonic deviceaccording to an example of the invention.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings which form a part hereof, and in which is shown,by way of illustration, specific embodiments in which the invention maybe practiced. In the drawings, like numerals describe substantiallysimilar components throughout the several views. These embodiments aredescribed in sufficient detail to enable those skilled in the art topractice the invention. Other embodiments may be utilized andstructural, or logical changes, etc. may be made without departing fromthe scope of the present invention.

In this work, we present recent developments in magnonic holographicmemory devices exploiting spin waves for information transfer. Exampledevices comprise a magnetic matrix and spin wave generating/detectingelements placed on the edges of the waveguides. The matrix consists of agrid of magnetic waveguides connected via cross junctions. Magneticmemory elements are incorporated within the junction while the read-inand read-out is accomplished by the spin waves propagating through thewaveguides. We present experimental data on spin wave propagationthrough NiFe and YIG magnetic crosses. The obtained experimental datashow prominent spin wave signal modulation (up to 20 dB for NiFe and 35dB for YIG) by the external magnetic field, where both the strength andthe direction of the magnetic field define the transport between thecross arms. We also present experimental data on the 2-bit magnonicholographic memory built on the double cross YIG structure withmicro-magnets placed on the top of each cross. It is possible torecognize the state of each magnet via the interference pattern producedby the spin waves with all experiments done at room temperature.Magnonic holographic devices aim to combine the advantages of magneticdata storage with wave-based information transfer. We present estimateson the spin wave holographic devices performance, including powerconsumption and functional throughput. According to the estimates,magnonic holographic devices may provide data processing rates higherthan 1×10¹⁸ bits/cm²/s while consuming 0.15 mW. Technological challengesand fundamental physical limits of this approach are also discussed.

I. Introduction

There is growing interest in novel computational devices able toovercome the limits of the currentcomplimentary-metal-oxide-semiconductor (CMOS) technology and providefurther increase of the computational throughput. A number of the“beyond CMOS” proposals are aimed at the development of new switchingtechnologies with increased scalability and improved power consumptioncharacteristics over the silicon transistor. However, it is difficult toexpect that a new switch will outperform CMOS in all figures of merit,and more importantly, will be able to provide multiple generations ofimprovement as was the case for CMOS. An alternative route to thecomputational power enhancement is via the development of novelcomputing devices, aimed not to replace, but to complement CMOS byspecial task data processing. Spin wave (magnonic) logic devices takethe advantages of the wave interference at nanometer scale and utilizephase in addition to amplitude for building logic units for paralleldata processing.

A spin wave is a collective oscillation of spins in a magnetic lattice,analogous to phonons, the collective oscillation of the nuclear lattice.The typical propagation speed of spin waves does not exceed 10⁷ cm/s,while the attenuation time at room temperature is about a nanosecond inthe conducting ferromagnetic materials (e.g. NiFe, CoFe) and may behundreds of nanoseconds in non-conducting materials (e.g. YIG). Such ashort attenuation time explains the lack of interest in spin waves as apotential information carrier in the past. The situation has changeddrastically as the technology of integrated logic circuits has scaleddown to the deep sub-micrometer scale, where the short propagationdistance of spin waves (e.g. tens of microns at room temperature) ismore than sufficient for building logic circuits. At the same time, spinwaves have several inherent appealing properties making them promisingfor building wave-based logic devices. For instance, spin wavepropagation can be directed by using magnetic waveguides similar tooptical waveguides. The amplitude and the phase of propagating spinwaves can be modulated by an external magnetic field. Spin waves can begenerated and detected by electronic components (e.g. multiferroics),which make them suitable for integration with conventional logiccircuits. Finally, the coherence length of spin waves at roomtemperature may exceed tens of microns, which allows for the utilizationof spin wave interference for logic functionality. Such a long coherencelength at room temperature is a result of the collective nature of spinwave phenomena, where a large number of spins precessing together areunited by strong exchange coupling. It makes spin waves much more proneto scattering than a single electron and resolves one of the mostdifficult problems of spintronics associated with the necessity topreserve spin orientation while transmitting information between thespin-based units.

With zero applied current, the spin waves in two branches interfereconstructively and propagate through the structure. The waves interferedestructively and do not propagate through the structure if a certainelectric current is applied. At some point, magnonic logic devicesresemble the classical field effect transistor, where the magnetic fieldproduced by the electric current modulates the propagation of the spinwave—an analog to the electric current. Spin waves can be combined withnano-magnetic logic to combine the advantages of non-volatile datastorage in magnetic memory and the enhanced functionality provided bythe spin wave buses. The use of spin wave interference makes it possibleto realize Majority gates (which can be used as AND or OR gates) and NOTgates with a fewer number of elements than is required fortransistor-based circuitry, promising the further reduction of the sizeof the logic gates. In one example three-input spin wave Majority gatesare realized. However, the integration of the spin wave buses withnano-magnets in a digital circuit, where the magnetization state of thenano-magnet is controlled by a spin wave has not yet been realized untilthis disclosure.

An alternative approach to spin wave-based logic devices is to buildnon-Boolean logic gates for special task data processing. The essence ofthis approach is to maximize the advantage of spin wave interference.Wave-based analog logic circuits are potentially promising for solvingproblems requiring parallel operation on a number of bits at time (i.e.image processing, image recognition). The concept of magnonicholographic memory (MHM) for data storage and special task dataprocessing has been recently proposed. Holographic devices for dataprocessing have been extensively developed in optics during the pastfive decades. The development of spin wave-based devices allows us toimplement some of the concepts developed for optical computing tomagnetic nanostructures utilizing spin waves instead of optical beams.There are certain technological advantages that make the spin waveapproach even more promising than optical computing. First, shortoperating wavelength (i.e. 100 nm and below) of spin wave devicespromises a significant increase of the data storage density (˜λ² for 2Dand ˜λ³ for 3D memory matrixes). Second, even more importantly, is thatspin wave bases devices can have voltage as an input and voltage as anoutput, which makes them compatible with the conventional CMOScircuitry. Though spin waves are much slower than photons, magnonicholographic devices may possess a higher memory capacity due to theshorter operational wavelength and can be more suitable for integrationwith the conventional electronic circuits.

The present disclosure shows recent experimental results on magnonicholographic memory and discuss the advantages and potential shortcomingsof this approach. The rest of the paper is organized as follows. InSection II, we describe the structure and the principle of operation ofmagnonic holographic memory. Next, we present experimental data on thefirst 2-bit magnonic holographic memory in Section III. The advantagesand the challenges of the magnonic holographic devices are discussed inthe Sections IV. In Section V, we present the estimates on thepractically achievable performance characteristics.

One example of a method of operating a memory or logic device is shownin FIG. 9. In operation 902, a holographic data point is formed usingspin wave interactions in a device. In operation 904, the data point isstored in the device. In operation 906, and the data point issubsequently read.

II. Material Structure and the Principle of Operation

The schematics of a MHM device are shown in FIG. 1(A). The core of thestructure is a magnetic matrix consisting of the grid of magneticwaveguides with nano-magnets placed on top of the waveguide junctions.Without loss of generality, we have depicted a 2D mesh of orthogonalmagnetic waveguides, though the matrix may be realized as a 3D structurecomprising the layers of magnetic waveguides of a different topology(e.g. honeycomb magnetic lattice). The waveguides serve as a media forspin wave propagation—spin wave buses. The buses can be made of amagnetic material such as yttrium iron garnet Y3Fe₂(FeO₄)₃ (YIG) orpermalloy (Ni₈₁Fe₁₉) ensuring maximum possible group velocity andminimum attenuation for the propagating spin waves at room temperature.The nano-magnets placed on top of the waveguide junctions act as memoryelements holding information encoded in the magnetization state. Thenano-magnet can be designed to have two or several thermally stablestates of magnetization, where the number of states defines the numberof logic bits stored in each junction. The spins of the nano-magnet arecoupled to the spins of the junction magnetic wires via the exchangeand/or dipole-dipole coupling affecting the phase of the propagation ofspin waves. The phase change received by the spin wave depends on thestrength and direction of the magnetic field produced by thenano-magnet. At the same time, the spins of the nano-magnet are affectedby the local magnetization change caused by the propagating spin waves.

The input/output ports are located at the edges of the waveguides. Theseelements are aimed to convert the input electric signals into spinwaves, and vice versa, convert the output spin waves into electricalsignals. There are several possible options for building such elementsby using micro-antennas spin torque oscillators, and multiferroicelements.

For example, the micro-antenna is a conducting contour placed in thevicinity of the spin wave bus. An electric current passed through thecontour generates a magnetic field around the current-carrying wires,which excites spin waves in the magnetic material, and vice versa, apropagating spin wave changes the magnetic flux from the magneticwaveguide and generates an inductive voltage in the antenna contour. Theadvantages and shortcomings of different input/output elements will bediscussed later in the text.

Spin waves generated by the edge elements are used for informationread-in and read-out. The difference among these two modes of operationis in the amplitude of the generated spin waves. In the read-in mode,the elements generate spin waves of a relatively large amplitude, so twoor several spin waves coming in-phase to a certain junction producemagnetic field sufficient for magnetization change within thenano-magnet. In the read-out mode, the amplitude of the generated spinwaves is much lower than the threshold value required to overcome theenergy barrier between the states of nano-magnets. So, the magnetizationof the junction remains constant in the read-out mode.

The formation of the hologram occurs in the following way. The incidentspin wave beam is produced by the number of spin wave generatingelements (e.g. by the elements on the left side of the matrix asillustrated in FIG. 1(B)). All the elements are biased by the same RFgenerator exciting spin waves of the same frequency, f and amplitude,A₀, while the phase of the generated waves are controlled by DC voltagesapplied individually to each element. Thus, the elements constitute aphased array allowing us to artificially change the angle ofillumination by providing a phase shift between the input waves.Propagating through the junction, spin waves accumulate an additionalphase shift, Δφ, which depends on the strength and the direction of thelocal magnetic field provided by the nano-magnet, H_(m):

${{\Delta \; \varphi} = {\int_{0}^{r}{{k\left( {\overset{\_}{H}}_{m} \right)}\ {r}}}},$

where the particular form of the wavenumber k(H) dependence varies formagnetic materials, film dimensions, the mutual direction of wavepropagation and the external magnetic field. For example, spin wavespropagating perpendicular to the external magnetic field (magnetostaticsurface spin wave—MSSW) and spin waves propagating parallel to thedirection of the external field (backward volume magnetostatic spinwave—BVMSW) may obtain significantly different phase shifts for the samefield strength. The phase shift Δφ produced by the external magneticfield variation δH in the ferromagnetic film can be expressed asfollows:

$\begin{matrix}{\frac{\Delta \; \varphi}{\partial\; H} = {{\frac{l}{d}{\frac{\; {\left( {\gamma \; H} \right)^{2} + \omega^{2}}}{\mspace{11mu} {2\pi \; \gamma^{2}M_{s}H^{2}}}\;}_{{({BVMSW})},}\frac{\Delta \; \varphi}{\partial\; H}} = {{- \frac{l}{d}}{\frac{\gamma^{2}\left( {H + {2\; \pi \; M_{s}}} \right)}{\omega^{2} - {\gamma^{2}{H\left( {H + {4\; \pi \; M_{s}}} \right)}}}\;}_{{({MSSW})},}}}} & (2)\end{matrix}$

where Δφ is the phase shift produced by the change of the externalmagnetic field δH, l is the propagation length, d is the thickness ofthe ferromagnetic film, γ is gyromagnetic ratio, ω=2πf, 4πM_(s) is thesaturation magnetization of the ferromagnetic film. The output signal isa result of superposition of all the excited spin waves travelingthrough the different paths of the matrix. The amplitude of the outputspin wave is detected by the voltage generated in the output element(e.g. the inductive voltage produced by the spin waves in the antennacontour). The amplitude of the output voltage is corresponding to themaximum when all the waves are coming in-phase (constructiveinterference), and the minimum when the waves cancel each other(destructive interference). The output voltage at each port depends onthe magnetic states of the nano-magnets within the matrix and theinitial phases of the input spin waves. In order to recognize theinternal state of the magnonic memory, the initial phases are varied(e.g. from 0 to π). The ensemble of the output values obtained at thedifferent phase combinations constitute a hologram which uniquelycorresponds to the internal structure of the matrix.

In general, each of the nanomagnets can have more than 2 thermallystable states, which makes it possible to build a multi-stateholographic memory device (i.e. z^(N) possible memory states, where z isthe number of stable magnetic states of a single junction and N is thenumber of junctions in the magnetic matrix). The practically achievablememory capacity depends on many factors including the operationalwavelength, coherence length, the strength of nano-magnets coupling withthe spin wave buses, and noise immunity. In the next Section, we presentexperimental data on the operation of the prototype 2-bit magnonicholographic memory.

III. Experimental Data

The set of experiments started with the spin wave transport study in asingle cross structure, which is the elementary building block for 2DMHM as depicted in FIG. 1. In FIG. 1, an example array 100 ofintersecting magnetic wave guides 102 is shown. A number of magnets 104are shown located at junctions of the intersecting magnetic wave guides102. Also shown in FIG. 1, are a number of spin wave generator/detectors106.

Two types of single cross devices made of Y₃Fe₂(FeO₄)₃ (YIG) andPermalloy (Ni₈₁Fe₁₉) were fabricated. Both of these materials arepromising for application in magnonic waveguides due to their highcoherence length of spin waves. At the same time, YIG and Permalloydiffer significantly in electrical properties (e.g. YIG is an insulator,permalloy is a conductor) and in fabrication method. YIG crossstructures 110 were made from single crystal YIG films epitaxially grownon top of Gadolinium Gallium Garnett (Gd₃Ga₅O₁₂) substrates using theliquid-phase transition process. After the films were grown,micro-patterning was done by laser ablation using a pulsed infraredlaser (λ≈1.03 μm), with a pulse duration of ˜256 ns. The YIG crossjunction has the following dimensions: the length of the whole structureis 3 mm; the width of the arm in 360 μm; thickness is 3.6 um. Permalloycrosses were fabricated on top of oxidized silicon wafers. The wafer wasspin coated with a 5214E Photoresist at 4000 rpm and exposed using aKarl Suss Mask Aligner. After development, a permalloy metal film wasdeposited via Electron-Beam Evaporation with a thickness of 100 nm andwith an intermediate seed layer of 10 nm of Titanium to increase theadhesion properties of the Permalloy film. Lift-off using acetonecompleted the process. Permalloy cross junction has the followingdimensions: the length of the whole structure is 18 um; the width of thearm in 6 μm; thickness is 100 nm.

Spin waves in YIG and Permalloy structures were excited and detected viamicro-antennas that were placed at the edges of the cross arms. Antennaswere fabricated from gold wire and mechanically placed directly at thetop of the YIG cross. In the case of permalloy, the conducting cross wasinsulated with a 100 nm layer of SiO₂ deposited via Plasma-EnhancedChemical Vapor Deposition (PECVD) and gold antennas were fabricatedusing the same photolithographic and lift-off procedure as with thepermalloy cross structures. A Hewlett-Packard 8720A Vector NetworkAnalyzer (VNA) was used to excite/detect spin waves within thestructures using RF frequencies. Spin waves were excited by the magneticfield generated by the AC electric current flowing through theantenna(s). The detection of the transmitted spin waves is via inductivevoltage measurements. Propagating spin waves change the magnetic fluxfrom the surface, which produces an inductive voltage in the antennacontour. The VNA allowed the S-Parameters of the system to be measured;showing both the amplitude of the signals as well as the phase of boththe transmitted and reflected signals. Samples were tested inside a GMW3472-70 Electromagnet system which allowed the biasing magnetic field tobe varied from −1000 Oe to +1000 Oe. The schematics of the experimentalsetup for spin wave transport study in the single cross structures areshown in FIG. 2.

First, we studied spin wave propagation between the four arms of thepermalloy cross-structure as shown in FIG. 3(A-B) under different biasmagnetic field. The input/output ports are numbered from 1 to 4 startingat the 9 O'clock position and then enumerated sequentially in along aclockwise direction. In order to define the angle between the externalmagnetic field and the direction of signal propagation, we define the Xaxis along the line from port 1 to port 3, and the Y axis along the linefrom port 4 to port 2 propagating as depicted in FIG. 2. Spin waves wereexcited on port 2 (the top of the magnetic cross) and read out from port4 (the bottom of the cross) (see FIG. 1). The graph in FIG. 3 shows thechange of the amplitude of the transmitted signal as a function of thestrength of the external magnetic field directed perpendicular to thepropagating spin waves as depicted in the inset to FIG. 3. Hereafter, weshow the relative change of the amplitude in decibels normalized to somevalue (e.g. to the maximum value). The normalization is needed as theinput power varies significantly for permalloy and YIG structures aswell as for the type of experiment. The reference transmission level istaken at 300 Oe, where the S₁₂ parameter is at its absolute maximum. Atsmall magnetic fields below 100 Oe a very small amplitude signal wasobserved. At approximately 150 Oe there is a noticeable increase in theamplitude followed by a plateau in the response as the field isincreased to 500 Oe. Also of interest is the response of the signal as afunction of the applied magnetic field direction. In FIG. 3(D), wepresent an example of the experimental data showing the influence of thedirection of the bias field on spin waves transport from port 2 to port4. The results demonstrate prominent change in the amplitude of thetransmitted signal [18 dB] when the field is applied between 20° and30°. The main observations of these experiments are the following. (i)Spin wave propagation through the cross junction can be efficientlycontrolled by the external magnetic field. (ii) Both the amplitude andthe direction of the magnetic field can be utilized for spin wavecontrol.

We conducted similar experiments on the YIG single cross device as shownin FIG. 4. It was observed that prominent signal modulation could bedetermined by the direction and the strength of the external magneticfield. In FIG. 4, there is shown an example of experimental data on thespin wave transport between ports 2 and 1. The maximum transmissionbetween the orthogonal arms occurs when the field is applied at 68°,while the minimum is seen when the field is applied at 0°. The On/Offratio for the YIG cross reaches 35 dB. Of noticeable interest is alsothe effect of non-reciprocal spin wave propagation. The two curves inFIG. 4(D) show signal propagation from port 2 to port 4, and in theopposite direction from port 4 to port 2. The measurements are done atthe same bias magnetic field of 998 Oe. There is a difference of about 5dB for the signals propagating in the opposite direction. The effect isobserved in a relatively narrow frequency range (e.g. from 5.2 GHz to5.4 GHz). Concluding on the spin wave transport in the permalloy and YIGsingle cross structures, prominent signal modulation has been observedin both cases. For the chosen parameters, the operation frequency isslightly higher for YIG structure (˜5 GHz) than for permalloy (˜3 GHz).The speed of signal propagation is slightly faster in permalloy (3.5×106cm/s) than in YIG (3.0×106 cm/s). The difference in the spin wavetransport can be attributed to the differences between the intrinsicmaterial properties of YIG and Permalloy as well as the difference inthe cross dimensions. It is important to note, that in both cases thelevel of the power consumption was at the microwatt scale (e.g. 0.1μW-1.0 μW for permalloy and 0.5 μW-5.0 μW for YIG) with no feasibleeffect of micro heating on the spin wave transport. The summary of theexperimental findings for permalloy and YIG single cross junctions cabbe found in Table I.

TABLE I Permalloy YIG Cross dimensions L = 18 μm, w = 6 μm, L = 3 mm, w= 300 μm, d = 100 nm d = 3.8 μm Operational Frequency 3 GHz-4 GHz 5GHz-6 GHz SW group velocity 3.5 × 10⁶ cm/s 3.0 × 10⁶ cm/s Maximum On/Off20 dB 35 dB ratio Power consumption 0.1 μW-1 μW  0.5 μW-5 μW Compatibility with Yes No Silicon

Next, we carried out experiments on spin wave transport and interferencein the double-cross structure 500 made of YIG as shown in FIG. 5. Thechoice of material is mainly due to the larger size of the structure andspin wave detecting antennas, where the larger the area of the detectingcontour results in higher the observed output inductive voltage. Themulti-port double-cross YIG structure is suitable for the study of spinwave interference. In this study, several coherent spin wave signalswere excited by ports 3, 4, 5 and 6 connected to one port of the VNA.The output is detected at port 1. The phase shifters were employed tovary the phase difference between the ports as shown in FIG. 5(B).

FIG. 6 show the experimental data on the output voltage collected in thefrequency range from 5.3 GHz to 5.5 GHz. The curves of the differentcolor correspond to the different phase shifts between the spin wavegenerated ports. Phase 1 represents a change in the phase of ports 4 and6 and Phase 2 represents a change in the phase of ports 3 and 5. FIGS.6(B-D) show the slices of data taken at a frequency of 5.385 GHz, 5.410GHz and 5.45 GHz, respectively. The black markers denoted by squaresdepict the experimentally obtained data, and the red markers denoted bycircles depict the theoretical output for the ideal case of theinterfering waves of the same frequency and amplitude. The theoreticaldata is normalized to have the same maximum value as the experimentaldata at phase difference zero (constructive interference). Experimentaldata shows an excellent fit with the theoretical predictions, whichimplies the dominant role of wave interference in the output signalformation. Discrepancies in the amplitude can be attributed to parasiticnoise which raises the base amplitude of the signal to greater thannonzero value even when the phase should be perfectly destructive.

The data presented in FIG. 7 are collected in the experiments wherePhase 2 (ports 3 and 5) was changed, while Phase 1 (ports 2 and 4) waskept constant. The ability to independently change the initial phases ofthe spin waves is equivalent to changing the angle of illumination forbuilding a holograms as illustrated in FIG. 1(B). In FIG. 7, we presentexperimental data showing the holographic image of the double-crossstructure without memory elements. The surface is a computerreconstructed 3-D plot showing the output voltage as a function of Phase1 and Phase 2. The excitation frequency is 5.40 GHz, the bias magneticfield is 1000 Oe. In this case, antennas on ports 2 and 4 generated spinwaves with the initial Phase 1, and antennas on ports 3 and 5 generatedspin waves with initial Phase 2. No signal is applied to port 1. Theoutput is detected at port 6. The change of the output inductive voltageis a result of spin wave interference. It has maximum values in the caseof the constructive interference (i.e. Phase 1=Phase 2, (0,0) or (π,π)),and shows minimum output signal when the waves are coming out-of-phase((0,π) or (π,0)).

Finally, we conducted experiments to demonstrate the operation of aprototype 2-bit magnonic holographic memory device. Two micro-magnetsmade of cobalt magnetic film were placed on top of the junctions of thedouble-cross YIG structure. As mentioned in Section II, these magnetsserve as a memory element, where the magnetic state represents logiczeroes and ones. The schematic of the double-cross structure withmicro-magnets attached are shown in FIG. 8(A). The length of each magnetis 1.1 mm, the width is 360 μm and each has a coercivity of 200-500Oersted (Oe). For the test experiments, we used four mutual orientationsof micro-magnets, where the magnets are oriented parallel to the axisconnecting ports 1-6, or the axis connecting 2-4; and two cases when themicro-magnets are oriented in the orthogonal directions. Holographicimages were collected for each case. FIG. 8 shows the collection of datacorresponding to output voltage obtained for different magneticconfigurations. The phases of the input elements are the same as in theprevious experiment. Markers of different shape and color in the legendof FIG. 8 represent the direction of the “north” end of the micromagnet. The output from the same structure varies significantly fordifferent phase combinations. In some cases, the magnetic states of themagnets can be recognized by just one measurement (e.g. (0,0) phasecombination). It is also possible that different magnetic states providealmost the same output (e.g. parallel and orthogonal magnetconfigurations measured at (π,0) phase combination).

The main observation we want to emphasize is the feasibility of parallelread-out and reconstruction of the magnetic state via spin waveinterference. As one can see from the data in FIG. 8(B), it is possibleto distinctly identify the magnetic states by changing the phases of theinterfering waves, which is similar to changing the angle of observationin a conventional optical hologram. We would like to emphasize that allexperiments reported in this Section are done at room temperature.

IV. Discussion

The obtained experimental data show the practical feasibility ofutilizing spin waves for building magnonic holographic logic devices andhelps to illustrate the advantages and shortcomings of the spin waveapproach. Of these results there are several important observations wewish to highlight.

First, spin wave interference patterns produced by multiple interferingwaves are recognized for a relatively long distance (more than 3millimeters between the excitation and detection ports) at roomtemperature. Coding information into the phase of the spin waves appearsto be a robust instrument for information transfer showing a negligibleeffect to thermal noise and immunity to the structures imperfections.This immunity to the thermal fluctuations can be explained by takinginto account that the flicker noise level in ferrite structures usuallydoes not exceed −130 dBm. At the same time, spin waves are not sensitiveto the structure's imperfections which have dimensions much shorter thanthe wavelength. These facts explain the good agreement between theexperimental and theoretical data (e.g. as shown in FIG. 6).

Second, spin wave transport in the magnetic cross junctions isefficiently modulated by an external magnetic field. Spin wavepropagation through the cross junction depends on the amplitude as wellas the direction of the external field. This provides a variety ofpossibilities for building magnetic field-effect logic devices forgeneral and special task data processing. Boolean logic gates such asAND, OR, NOT can be realized in a single cross structure, where anapplying external field exceeding some threshold stops/allows spin wavepropagation between the selected arms. The ability to modulate spin wavepropagation by the direction of the magnetic field is useful forapplication in non-Boolean logic devices. It is important to note thatin all cases the magnitude of the modulating magnetic field is of theorder of hundreds of Oersteds, which can be produced by micro- andnano-magnets.

Finally, it appears possible to recognize the magnetic state of themagnet placed on the top of the cross junction via spin waves, whichintroduces an alternative mechanism for magnetic memory read out. Thisproperty itself may be utilized for improving the performance ofconventional magnetic memory devices. However, the fundamental advantageof the magnonic holographic memory is the ability to read-out a numberof magnetic bits in parallel though the obtained experimental datademonstrates the parallel read-out of just two magnetic bits. In therest of this Section, we discuss the fundamental limits and thetechnological challenges of building multi-bit magnonic holographicdevices and present the estimates on the device performance.

We start the discussion with the choice of magnetic material forbuilding spin waveguides. There are two materials that have becomepredominant, permalloy (N₈₁Fe₁₉) and YIG, for spin wave devicesprototyping. The coherence length of spin waves in permalloy is abouttens of microns at room temperature while the coherence length in anon-conducting YIG exceeds millimeters. The attenuation time for spinwaves at room temperature is about a nanosecond in permalloy and ahundreds of nanoseconds in YIG. However, the fabrication of YIGwaveguides may require a special gadolinium gallium garnet (GGG)substrate. In contrast, a permalloy film can be deposited onto a siliconplatform by using the sputtering technique. Though YIG has betterproperties in terms of the coherence length and a lower attenuation,permalloy is more convenient for making magnonic devices on a siliconsubstrate.

In order to make a multi-bit magnonic holographic devices, the operatingwavelength should be scaled down below 100 nm. The main challenge withshortening the operating wavelength is associated with the building ofnanometer-scale spin wave generating/detecting elements. There areseveral possible ways of building input/output elements by usingmicro-antennas, spin torque oscillators, and multi-ferroic elements. Sofar, micro-antennas are the most convenient and widely used tool forspin wave excitation and detection in ferromagnetic films. Reducing thesize of the antenna will lead to the reduction of the detected inductivevoltage. This fact limits the practical application of any types ofconducting contours for spin wave detection. The utilization of spintorque oscillators makes it possible to scale down the size of theelementary input/output port to several nanometers. The main challengefor the spin torque oscillators approach is to reduce the currentrequired for spin wave generation. More energetically efficient are thetwo-phase composite multiferroics comprising piezoelectric andmagnetostrictive materials.

An electric field applied across the piezoelectric produces stress,which, in turn, affects the magnetization of the magnetoelasticmaterial. The advantage of the multiferroic approach is that themagnetic field required for spin wave excitation is produced viamagneto-electric coupling by applying an alternating electric fieldrather than an electric current. For example, in Ni/PMN-PT syntheticmultiferroic, an electric field of 0.6MV/m may be applied across thePMN-PT in order to produce 90 degree magnetization rotation in Nickel.Such a relatively low electric field required for magnetization rotationtranslates in ultra-low power consumption for spin wave excitation. Atthe same time, the dynamics of the synthetic multiferroics, especiallyat the nanometer scale, remains mostly unexplored.

To benchmark the performance of the magnonic holographic devices, weapply a charge-resistance approach. The details of the estimates and thekey assumptions are given in Appendix A. According to the estimates, MHMdevice consisting of 32 inputs, with a 60 nm separation distance betweenthe inputs would consume as low as 150 μW of power or 72 fJ percomputation. At the same time, the functional throughput of the MHMscales proportional to the number of cells per area/volume and exceeds1.5×10¹⁸ bits/cm²/s for a 60 nm feature size. It is interesting to note,that holographic logic units can be used for solving certainnondeterministic polynomial time (NP) class of problems (i.e. findingthe period of the given function). The efficiency of holographiccomputing with classical waves is somewhere intermediate between digitallogic and quantum computing, allowing us to solve a certain class ofproblems fundamentally more efficient than general-type processors butwithout the need for quantum entanglement. Image recognition andprocessing are among the most promising applications of magnonicholographic device exploiting its ability to process a large number ofbits/pixels in parallel within a single core.

It may be expected that the amplitude/phase of the redirected (bended)spin wave depends on the wavelength/size ratio, the material propertiesof the cross, and magnetic field produced by the nano-magnet. Weattribute the change in the interference pattern to the different phaseshifts accumulated by spin waves propagating under the nano-magnets ofdifferent orientation (i.e. Eqs. 1-2).

CONCLUSIONS

The collected experimental data show rich physical phenomena associatedwith spin wave propagation in single- and double-cross structures.Prominent signal modulation by the direction, rather than the amplitudeof magnetic field and the low effect of thermal noise on spin wavepropagation at room temperature are among the many interesting findingspresented here. The effect of spin wave redirection between the crossarms by the external magnetic field may be further exploited forbuilding a variety of logic devices. Besides, spin waves appear to be arobust instrument allowing us to sense the magnetic state ofmicro-magnets by the change in the interference pattern. It is possibleto recognize the unique holographic output for the differentorientations of micro-magnets in a relatively long device at roomtemperature. Overall, the obtained data demonstrates building magnonicholographic devices. In one example, these holographic devices may beaimed not to replace but to complement CMOS in special type dataprocessing such as speech recognition and image processing. According toestimates, scaled magnonic holographic devices may provide more than1×10¹⁸ bits/cm²/s data processing rate while consuming less than 0.2 mWof energy. The development of scalable magnonic holographic devices andtheir incorporation with conventional electronic devices may pave theroad to the next generations of logic devices with functionalcapabilities far beyond current CMOS.

FIG. 10 shows an example electronic device incorporating magnonic memoryaccording to an embodiment of the invention. FIG. 10 shows a magnonicmemory device 1002 and a complementary metal oxide device 1020. Themagnonic memory device 1002 is coupled to the complementary metal oxidedevice 1020 with communication pathway 1012. In the example of FIG. 10,the magnonic memory device 1002 includes an array of intersectingmagnetic wave guides 1004, and spin wave generator/detectors 1006, 1008located at a periphery of the array 1004. The example of FIG. 10 furtherincludes circuitry 1010 to covert electrical signals to spin waves andto convert spin waves to electrical signals.

To better illustrate the method and apparatuses disclosed herein, anon-limiting list of embodiments is provided here:

Example 1 includes a memory device, comprising an array of intersectingmagnetic wave guides, a number of magnets located at junctions of theintersecting magnetic wave guides, and spin wave generator/detectorslocated at a periphery of the array and coupled to the intersectingmagnetic wave guides.

Example 2 includes the memory device of example 1, further includingcircuitry to covert electrical signals to spin waves and to convert spinwaves to electrical signals.

Example 3 includes the memory device of any one of examples 1-2, whereinthe circuitry is configured to control both phase and amplitude of thespin waves.

Example 4 includes the memory device of any one of examples 1-3, whereinthe array of intersecting magnetic wave guides includes a 2-dimensionalarray.

Example 5 includes the memory device of any one of examples 1-4, whereinthe array of intersecting magnetic wave guides includes a 3-dimensionalarray.

Example 6 includes the memory device of any one of examples 1-5, whereineach magnet in the number of magnets is capable of two states.

Example 7 includes the memory device of any one of examples 1-6, whereineach magnet in the number of magnets is capable of more than two states.

Example 8 includes an electronic device, comprising a complementarymetal oxide device and a magnonic memory device coupled to thecomplementary metal oxide device, the magnonic memory device includingan array of intersecting magnetic wave guides, a number of magnetslocated at junctions of the intersecting magnetic wave guides, spin wavegenerator/detectors located at a periphery of the array and coupled tothe intersecting magnetic wave guides, and circuitry to covertelectrical signals to spin waves and to convert spin waves to electricalsignals.

Example 9 includes the electronic device of example 8, wherein the CMOSdevice includes a processor.

Example 10 includes the electronic device of any one of examples 8-9,wherein the CMOS device includes a memory device.

Example 11 includes the electronic device of any one of examples 8-10,wherein the array of intersecting magnetic wave guides include yttriumiron garnet wave guides.

Example 12 includes the electronic device of any one of examples 8-11,wherein the array of intersecting magnetic wave guides include permalloywave guides.

Example 13 includes the electronic device of any one of examples 8-12,wherein the permalloy wave guides are formed on silicon.

Example 14 includes the electronic device of any one of examples 8-13,wherein the spin wave generator/detectors include micro-antennae.

Example 15 includes the electronic device of any one of examples 8-14,wherein the spin wave generator/detectors include spin torqueoscillators.

Example 16 includes the electronic device of any one of examples 8-15,wherein the spin wave generator/detectors include multiferroticelements.

Example 17 includes a method, comprising forming a holographic datapoint using spin wave interactions in a device, storing the data pointin the device, and reading the data point.

Example 18 includes the method of example 17, wherein storing the datapoint includes storing the data point in a magnet located at anintersection of magnetic wave guides in an array.

Example 19 includes the method of any one of examples 17-18, furtherincluding converting at least one electrical signal to a spin wave tostore the data point.

Example 20 includes the method of one of examples 17-19, furtherincluding converting a spin wave to an electrical signal when readingthe data point.

Appendix A

This section contains the details on the power consumption estimates. Weassume that the input to each magnetoelectric (ME) cell is an AC voltagewith amplitude created in a RLC oscillator. Then the power dissipationon resonance is

$\begin{matrix}{P_{in} = {\frac{V_{in}^{2}}{2\; R}.}} & (1)\end{matrix}$

The amplitude of the electric field in the piezoelectric of thicknesst_(pz) is

E _(in) ≦V _(in) /t _(pz).  (2)

The amplitude of strain created in the piezoelectric of the ME cell is

∈_(xx) =d ₃₁ E _(in),  (3)

where the piezoelectric coefficient is d₃₁. Hereafter, it is assumedthat spin wave is propagating along the X axis as shown in the inset toFIG. 2. The stress transferred to the ferromagnet is

σ=Y∈ _(xx),  (4)

where the Young's modulus of the piezoelectric is Y. The change in themagnetic anisotropy due to magnetostriction is

$\begin{matrix}{{U_{ms} = {\frac{3}{2}\lambda \; \sigma}},} & (5)\end{matrix}$

where the magnetostriction coefficient of the ferromagnet is λ. Then themaximum amplitude of magnetization change is

$\begin{matrix}{{\Delta \; M_{y}} \approx \frac{2\; U_{ms}}{\mu_{0}M_{s}}} & (6)\end{matrix}$

where the permeability of vacuum is μ₀, and the saturation magnetizationis M_(s). This can be expressed via the magnetoelectric coefficient

$\begin{matrix}{\alpha \approx \frac{\mu_{0}\Delta \; M_{y}}{E_{m}} \approx {\frac{3\; \lambda \; {Yd}_{31}}{M_{z}}.}} & (7)\end{matrix}$

Then the generated dimensionless amplitude of the spin wave can beapproximated as follows

$\begin{matrix}{{A_{m} = {\frac{\Delta \; M_{x}}{M_{s}} \approx \frac{\alpha \; V_{m}}{{\mu_{0}M_{s}t_{ps}}\;}}},} & (8)\end{matrix}$

The spin waves interact and attenuate as they propagate. If the distancebetween inputs is L, the number of inputs is N, and the attenuationlength is l_(at), then the propagation distance is

L _(tot) =NL  (9)

and let the minimum amplitude needed to be detected is a quarter of theaverage output amplitude

$\begin{matrix}{A_{\min}\frac{A_{in}}{4}\exp \; {\left( {- \frac{L_{tot}}{l_{at}}} \right).}} & (10)\end{matrix}$

If the group velocity of the spin waves is τ=L_(tot)/C_(sw), then thetime needed for one holographic imaging is

τ=NL/c _(sw).  (11)

Assuming that the detection occurs by the inverse of the ME effect, andthat its coefficients are the same as for the direct ME effect, weobtain that the connection between the magnetization amplitude and theamplitude of the generated electric field

$\begin{matrix}{\alpha \approx {\frac{ɛ_{yz}ɛ_{0}E_{\min}}{\Delta \; M}.}} & (12)\end{matrix}$

Thus the minimum output voltage is

$\begin{matrix}{V_{\min} = {{E_{\min}t_{pz}} = {\frac{\alpha \; M_{z}A_{\min}t_{pz}}{ɛ_{pz}ɛ_{0}}.}}} & (13)\end{matrix}$

Combining expressions (10) and (13), we have the following for voltages

$\begin{matrix}{V_{\min} = {\frac{V_{in}}{4}{\exp \left( {- \frac{NL}{l_{at}}} \right)}{\frac{\alpha^{2}}{ɛ_{pz}ɛ_{0}\mu_{0}}.}}} & (14)\end{matrix}$

Then the total driving power for N inputs is

$\begin{matrix}{{P_{tot} = {\frac{{NV}_{in}^{2}}{2\; R} = {\frac{8\; {NV}_{\min}^{2}}{R}\exp \; \left( \frac{2\; {NL}}{l_{at}} \right)\frac{ɛ_{n}^{2}}{c^{4}\alpha^{4}}}}},} & (15)\end{matrix}$

where C is the speed of light. For minimum detectability, the outputvoltage should exceed the Johnson noise voltage by 5×. The spectraldensity of noise is

V _(s) ²=4k _(B) TR.  (16)

The required power within the bandwidth B (approximately equal to the acvoltage frequency) is

$\begin{matrix}{P_{tot} = {800\; {NBk}_{B}{T_{\exp}\left( \frac{2\; {NL}}{I_{at}} \right)}{\frac{ɛ_{n}^{2}}{c^{4}\alpha^{4}}.}}} & (17)\end{matrix}$

And the total energy for one imaging is

E _(tot) =P _(tot)τ.  (18)

Using the magnetostriction parameters for the most advantageous case ofTerfenol-D and PMN-PT, the magnetoelectric coefficient

α=57 ns/m≈17/c.  (19)

The dielectric constant of PMN-PT is now ∈_(pz)=100 Substituting theparameters of the holographic system: N=32, L=60 nm, C_(sw)=4000 m/s,B=100 GHz, l_(at)=24 μm, we obtain:

τ=480 ps, P _(tot)=150 μW, E _(tot)=72 fJ.

While a number of advantages of embodiments described herein are listedabove, the list is not exhaustive. Other advantages of embodimentsdescribed above will be apparent to one of ordinary skill in the art,having read the present disclosure. Although specific embodiments havebeen illustrated and described herein, it will be appreciated by thoseof ordinary skill in the art that any arrangement which is calculated toachieve the same purpose may be substituted for the specific embodimentshown. This application is intended to cover any adaptations orvariations of the present invention. It is to be understood that theabove description is intended to be illustrative, and not restrictive.Combinations of the above embodiments, and other embodiments will beapparent to those of skill in the art upon reviewing the abovedescription. The scope of the invention includes any other applicationsin which the above structures and fabrication methods are used. Thescope of the invention should be determined with reference to theappended claims, along with the full scope of equivalents to which suchclaims are entitled.

What is claimed is:
 1. A memory device, comprising: an array ofintersecting magnetic wave guides; a number of magnets located atjunctions of the intersecting magnetic wave guides; and spin wavegenerator/detectors located at a periphery of the array and coupled tothe intersecting magnetic wave guides.
 2. The memory device of claim 1,further including circuitry to covert electrical signals to spin wavesand to convert spin waves to electrical signals.
 3. The memory device ofclaim 1, wherein the circuitry is configured to control both phase andamplitude of the spin waves.
 4. The memory device of claim 1, whereinthe array of intersecting magnetic wave guides includes a 2-dimensionalarray.
 5. The memory device of claim 1, wherein the array ofintersecting magnetic wave guides includes a 3-dimensional array.
 6. Thememory device of claim 1, wherein each magnet in the number of magnetsis capable of two states.
 7. The memory device of claim 1, wherein eachmagnet in the number of magnets is capable of more than two states. 8.An electronic device, comprising: a complementary metal oxide device;and a magnonic memory device coupled to the complementary metal oxidedevice, the magnonic memory device including: an array of intersectingmagnetic wave guides; a number of magnets located at junctions of theintersecting magnetic wave guides; spin wave generator/detectors locatedat a periphery of the array and coupled to the intersecting magneticwave guides; and circuitry to covert electrical signals to spin wavesand to convert spin waves to electrical signals.
 9. The electronicdevice of claim 8, wherein the CMOS device includes a processor.
 10. Theelectronic device of claim 8, wherein the CMOS device includes a memorydevice.
 11. The electronic device of claim 8, wherein the array ofintersecting magnetic wave guides include yttrium iron garnet waveguides.
 12. The electronic device of claim 8, wherein the array ofintersecting magnetic wave guides include permalloy wave guides.
 13. Theelectronic device of claim 12, wherein the permalloy wave guides areformed on silicon.
 14. The electronic device of claim 8, wherein thespin wave generator/detectors include micro-antennae.
 15. The electronicdevice of claim 8, wherein the spin wave generator/detectors includespin torque oscillators.
 16. The electronic device of claim 8, whereinthe spin wave generator/detectors include multiferrotic elements.
 17. Amethod, comprising: forming a holographic data point using spin waveinteractions in a device; storing the data point in the device; andreading the data point.
 18. The method of claim 17, wherein storing thedata point includes storing the data point in a magnet located at anintersection of magnetic wave guides in an array.
 19. The method ofclaim 17, further including converting at least one electrical signal toa spin wave to store the data point.
 20. The method of claim 17, furtherincluding converting a spin wave to an electrical signal when readingthe data point.